Combined Probability in Complex Event Patterns
Consider three events A, B, and C with the following probabilities: \( P(A)=0.3 \), \( P(B)=0.4 \), \( P(C)=0.5 \). The probabilities of the pairwise intersections are: \( P(A\cap B)=0.1 \), \( P(A\cap C)=0.15 \), and \( P(B\cap C)=0.12 \). The probability of the intersection of all three events is \( P(A\cap B\cap C)=0.05 \). […]
Part a
Determine the probabilities for the regions where exactly two of the events occur. Calculate: – The probability of \( A\cap B \) occurring, but not C. – The probability of \( A\cap C \) occurring, but not B. – The probability of \( B\cap C \) occurring, but not A.